By the way, while [itex]\sqrt{(x_1-x_0)^2+ (y_1-y_0)^2}[/itex] is the "standard metric" it would be equivalent to show the "for every [itex]\epsilon>0[/itex] there exist [itex]\delta> 0[/itex] such that max (|x-1|,|y-1|)< [itex]\delta[/itex] implies that |x2+ xy+ y- 3|<[itex]\epsilon[/itex] and might be simpler. Of course, your teacher might require that you be able to show that they are equivalent!